Control problem for diffusion-type random fields
type: Item
instance of: scholarly article
title: Control problem for diffusion-type random fields
zbMATH Open document ID: 0844.93079
DOI: 10.1007/BF02366795
author: Pavel S. Knopov
author: E. N. Derieva
published in: Cybernetics and Systems Analysis
publication date: 1996-03-27T00:00:00Z
review text: The following optimal control problem for a stochastic differential equation \[ \xi (t,s) = \xi_0 + \int^t_0 \int^s_0 a(x,y, \xi, u) dx dy + \int^t_0 \int^s_0 b(x,y, \xi) W(dx dy), \] \[ F(u) = \mathbb{E} \Biggl( \int^1_0 \int^1_0 f(t,s, \xi^u (t,s), u(t,s) \xi^u (t,s)) dt ds \Biggr) \to \min \] \vskip2mm is considered. For this problem, sufficient conditions for the existence of optimal controls, derived by Girsanov's method of transformation of measures, are given. Also the existence of \(\varepsilon\)-optimal controls is proved and a method for their construction is described.
reviewed by: Wiesław Kotarski
Mathematics Subject Classification ID: 93E20
zbMATH DE Number: 844530
zbMATH Keywords: \(\varepsilon\)-optimal controls
zbMATH Keywords: optimal control problem
zbMATH Keywords: stochastic
zbMATH Keywords: sufficient conditions
MaRDI profile type: Publication
cites work: Q3927983
cites work: Q3825879
cites work: Q4174610
cites work: Q4747316
cites work: Q3790506
cites work: Q3927984
cites work: Stochastic integrals in the plane
cites work: Dynamic Programming Conditions for Partially Observable Stochastic Systems
cites work: Necessary and Sufficient Dynamic Programming Conditions for Continuous Time Stochastic Optimal Control
full work available at URL: https://doi.org/10.1007/bf02366795
OpenAlex ID: W4251975150
description: scientific article; zbMATH DE number 844530